Targeted modal response control of structures using inerter systems based on master oscillator principle. (15th September 2021) - Zhang, Ruifu; Zhang, Luqi; Pan, Chao; De Domenico, Dario; Chen, Qingjun
Highlights: Targeted mode control algorithm for structures using inerter systems is proposed. Master oscillator principle is given to account for peculiar control mechanism of inerters. Specified modes are controlled without changing the characteristics of other modes. Closed-form expressions of design parameters of inerter-based systems are obtained. Abstract: Although the first modal response generally dominates in structural vibration control, higher-order mode control or multiple-mode control should also be taken into account when higher-order modes are excited. An effective way to accomplish multiple-mode control is to resort to inertial vibration absorbers, wherein the inerter serves as a two-terminal device with dynamic mass amplification and damping enhancement effects. Although previously published studies focused on inerter-based multiple-mode control, analytical design formulae have not been proposed owing to the peculiar mechanism of the inerter. Inspired by the two-terminal, relative-acceleration-related characteristics of the inerter, this study proposes a closed-form design formulation to identify the parameters of inerter systems to achieve targeted multiple-mode control. In this method, the relative deformation at the installation location is considered as the master degree-of-freedom, and the shape of the targeted control mode is considered as a structural deformation shape. In this way, by transforming the complex original structure into a master oscillator with the inerter, the parameters needed for the targeted-mode control can be easily determined based on the use of closed-form design formulae. The proposed targeted control method is applied to a benchmark 10-story building to illustrate how the parameters of inerter systems are designed by the proposed demand-oriented, targeted control method. The comparative analyses between the proposed and previous methods are conducted to demonstrate its superiority. The reductions of the designed inertances compared with alternative methods exceed 90%. Results show that the designed inerter systems can accurately and efficiently realize the targeted control of specific, multiple modal responses. The proposed method is proved to yield a high-precision, targeted-mode control effect, and requires relatively low computational effort. Therefore, it can be easily implemented in an inerter-based, multiple-mode control system. Graphical abstract: Image, graphical abstract